It is considerably older than Dryptosaurus but the
latter is said to be a relic of the Cenomanian, when
Asian tyrannosauroid immigrants became isolated in
eastern America.

I think you may be overlooking the fact that the earliest evidence of
tyrannosauroids comes from outside of Asia. We have two putative
tyrannosauroids of Late Jurassic age: _Stokesosaurus_ from Utah and
_Aviatyrannis_ from Portugal.

A highly derived braincase (for its Late Jurassic age) that was referred to
_Stokesosaurus_ is probably tyrannosauroid. Time will tell if it really
belongs to _Stokesosaurus_ (I would bet that it does; but I would also bet
that the very primitive-looking jaw fragment does not.)

_Iliosuchus_ (Middle Jurassic, England) may represent an early
tyrannosauroid; but we need something more than the ilia to go on.

As David mentioned, we also have EK tyrannosauroids from Europe
(_Eotyrannus_), as well as North America (teeth), and possibly Sth America
(_Santanaraptor_). And of course, China (_Dilong_).

The "Asian tyrannosauroid immigrant" hypothesis may be correct, but it
requires more evidence, and has a few bugs to work out.